9789048127849 - nonlinear least squares for inverse problems: theoretical foundations and step-by-step guide for applications (scientific computation) von chavent, guy (5 Ergebnisse)
Sprache: Englisch
Verlag: Springer, 2009
- Hardcover
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Sprache: Englisch
Verlag: FisicalBook, 2009
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Zustand: Like New. Used - Like New. This is a brand new book! Your purchase helps support Sri Lankan Children's Charity 'The Rainbow Centre'. Our donations to The Rainbow Centre have helped provide an education and a safe haven to hundreds of children who live in appalling conditions.
Sprache: Englisch
Verlag: Springer Verlag, 2009
- Hardcover
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Hardcover. Zustand: Brand New. 2010 edition. 374 pages. 9.00x6.00x0.75 inches. In Stock.
Sprache: Englisch
Verlag: Springer, 2009
- Hardcover
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Buch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - The domain of inverse problems has experienced a rapid expansion, driven by the increase in computing power and the progress in numerical modeling. When I started working on this domain years ago, I became somehow fr- tratedtoseethatmyfriendsworkingonmodeli…ngwhereproducingexistence, uniqueness, and stability results for the solution of their equations, but that I was most of the time limited, because of the nonlinearity of the problem, to provethatmyleastsquaresobjectivefunctionwasdi erentiable.Butwith my experience growing, I became convinced that, after the inverse problem has been properly trimmed, the nal least squares problem, the one solved on the computer, should be Quadratically (Q)-wellposed,thatis,both we- posed and optimizable: optimizability ensures that a global minimizer of the least squares function can actually be found using e cient local optimization algorithms, and wellposedness that this minimizer is stable with respect to perturbation of the data. But the vast majority of inverse problems are nonlinear, and the clas- cal mathematical tools available for their analysis fail to bring answers to these crucial questions: for example, compactness will ensure existence, but provides no uniqueness results, and brings no information on the presence or absenceofparasiticlocalminimaorstationarypoints.
Sprache: Englisch
Verlag: Springer Nature B.V., 2009
- Hardcover
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Zustand: Sehr gut. Zustand: Sehr gut | Seiten: 376 | Sprache: Englisch | Produktart: Bücher | This book provides an introduction into the least squares resolution of nonlinear inverse problems. The first goal is to develop a geometrical theory to analyze nonlinear least square (NLS) problems with respect to their quadratic wellp…osedness, i.e. both wellposedness and optimizability. Using the results, the applicability of various regularization techniques can be checked. The second objective of the book is to present frequent practical issues when solving NLS problems. Application oriented readers will find a detailed analysis of problems on the reduction to finite dimensions, the algebraic determination of derivatives (sensitivity functions versus adjoint method), the determination of the number of retrievable parameters, the choice of parametrization (multiscale, adaptive) and the optimization step, and the general organization of the inversion code. Special attention is paid to parasitic local minima, which can stop the optimizer far from the global minimum: multiscale parametrization is shown to be an efficient remedy in many cases, and a new condition is given to check both wellposedness and the absence of parasitic local minima. For readers that are interested in projection on non-convex sets, Part II of this book presents the geometric theory of quasi-convex and strictly quasi-convex (s.q.c.) sets. S.q.c. sets can be recognized by their finite curvature and limited deflection and possess a neighborhood where the projection is well-behaved.Throughout the book, each chapter starts with an overview of the presented concepts and results.
